Elastic virtual photoproduction of charmonia on nucleons is calculated in a parameter free way with the light‐cone dipole formalism and the same input: factorization in impact parameters, light‐cone wave functions for the photons and the charmonia, and the universal phenomenological dipole cross section which is fitted to other data. The charmonium wave functions are calculated with four known realistic potentials, and two models for the dipole cross section are tested. Very good agreement with data for the cross section of charmonium electroproduction is found in a wide range ofsandQ2. Using the ingredients from those calculations we calculate also exclusive electroproduction of charmonia off nuclei. Here new effects become important, (i) color filtering of thecc¯pair on its trajectory through nuclear matter, (ii) dependence on the finite lifetime of thecc¯fluctuation (coherence length) and (iii) gluon shadowing in a nucleus compared to the one in a nucleon. Total coherent and incoherent cross sections for C, Cu and Pb as functions ofsare presented. The results can be tested with future electron‐nucleus colliders or in the peripheral collisions of relativistic heavy ions. © 2003 American Institute of Physics